The popularity of digital signal processing has caused widespread application of analog to digital converters (ADCs) in modern communication systems. Digital signal processing is utilized in many different applications, such as signal (data, speech, video, etc.) processing, high-speed data converters, radar systems, data communication devices, such as receivers and transmitters and the like.
Moreover, recent demands for sensing wideband analog signals that emerge in various communication systems such as, radar system, cognitive radio systems, ultra-wideband communication systems and the like is forcing the conventional Nyquist rate ADCs towards their performance limits. This is due to the fact that conventional ADCs need to sample analog signals at rates greater than twice the bandwidth of the signal to ensure stable reconstruction of the digitized according to the Nyquist sampling theorem. In many applications, sampling at the Nyquist rate is inefficient because the signals of interest contain only a small number of significant frequencies relative to the band limit, although the locations of the frequencies may not be known a priori.
Additionally, the emerging theory of Compressive Sensing (CS) has shown that this reconstruction to be an inefficient strategy for acquiring signals that have a sparse or compressible representation in terms of an arbitrary basis.
Fortunately, most wideband signals that appear in many practical applications (for example, radar, cognitive radio and ultra-wideband communication systems) are spectrally sparse in the sense that their frequency support includes several limited intervals, spread over a wide spectrum. Although the theory of CS is already developed for discrete signals, research is still ongoing to propose efficient architectures and processes for practical Analog-to-Information Conversion (AIC) techniques that leverage the CS theory to acquire sparse/compressible analog signals at rates reduced far below the Nyquist rate.
Analog (pre-filter) sub-banding followed by Nyquist sampling of analog sub-bands and sub-band channel equalization is commonly invoked to overcome analog-to-digital converter dynamic range limitations. This approach employs a massively parallel implementation wherein the wide frequency region of interest is partitioned into sub-bands by parallel analog band-pass filters. It also requires equalization among adjacent analog sub-band partitions. Also, random demodulation combined with compressive sensing has been proposed for detecting an unknown signal somewhere in a large spectral region. This is a classical single channel random demodulator followed by compressive sensing to unwrap the aliased narrow-band spectrum resulting from under sampling. This approach works for detection of sparse (narrow-band) signals across the wide band of interest, however, it is not suitable for recovery of wideband signals.
FIG. 1 is an exemplary block diagram of a conventional channelized receiver. As shown, a wide band input analog signal X(t), for example, with a frequency of 4 GHz is input to an anti-aliasing filter 102 to reject signals outside of the band of interest. The anti-aliasing bandpass filter (BPF) 102 filter attenuates signals outside of the spectrum of interest. A full Nyquist rate analog-to-digital converter (ADC) 104 with a sampling frequency Fs, equal to or greater than the Nyquist frequency of the input signal, samples the output of the anti-aliasing filter, converting the analog signal to a digital signal. The output of the ADC 104 is then channelized by a (fixed resolution) filter bank 106. The full Nyquist rate ADC 104 samples the entire signal spectrum of interest. Sampled data are separated via the uniform fixed bandwidth filter 106. The filter bank (channelizer) 106 decomposes the wideband signal into equally spaced partitions. Estimated X(t) suffers from ADC dynamic range (maximum to minimum signal) limitation; and distortion (ripple & group delay) of signals wider than the channelizer fixed filter bandwidth.
However, many of the previously proposed approaches to Sub-Nyquist sampling of wideband signals, such as the above-described channelized receiver, require a priori knowledge of the number and locations of the occupied spectral bands and are computationally complex. Also, many of the proposed architectures to implement such approaches provide only an estimate of the sparsely occupied spectrum and are not capable of recovering the underlying wideband signal from the compressive samples.